Course detail

Mathematics 1

FAST-BAA101Acad. year: 2026/2027

The goal of the course is to deepen and strengthen the knowledge gained from high school math. Students will learn new techniques and mathematical methods, enhance their logical thinking, which will allow them to think and apply the knowledge they've gained in their specializations. Students should also learn to analyze a problem, choose the right approach, select the appropriate calculation method, and evaluate the result, which should lead to critical thinking. The course is divided into three topics: the first focuses on the basics of linear algebra; the second covers single-variable calculus; and the third is dedicated to the basics of integral calculus.

Language of instruction

Czech

Number of ECTS credits

6

Mode of study

Not applicable.

Guarantor

doc. Mgr. Irena Hinterleitner, Ph.D.

Department

Institute of Mathematics and Descriptive Geometry (MAT)

Entry knowledge

High school math knowledge is required.

Rules for evaluation and completion of the course

Attendance at the exercises is mandatory and monitored. The exercises include two credit tests in the 6th and 11th weeks of the semester. To get credit, students need to score at least 40% of the total points from both credit tests. Students who don’t reach the required points will be allowed to take a makeup credit test.

The exam will be written. It will include 4 problems, and students will have 90 minutes to solve them. The grading will follow the ECTS scale according to the table in the VUT Study and Examination Regulations.

Aims

Professional Knowledge:

  • Familiarity with matrix algebra and its application to solving systems of linear equations. Understanding of the fundamental concepts of differential and integral calculus of functions of one variable, including the geometric interpretation of selected concepts. Introduction to vector calculus and its applications.

Professional Skills:

  • The student will acquire proficiency in differentiation and integration techniques and will learn how to analyze the behavior of functions.
  • The student will be able to perform matrix operations, carry out elementary matrix transformations, compute determinants and inverse matrices, and solve systems of linear algebraic equations using both the Gaussian elimination method and inverse matrices.

General Competences:

  • The student will be prepared to continue further studies that require knowledge and understanding of the topics covered in this course.

Study aids

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

BUDÍNSKÝ, B. - CHARVÁT, J.: Matematika I. Praha, SNTL, 1987. (CS)
LARSON, R.- HOSTETLER, R.P.- EDWARDS, B.H.: Calculus (with Analytic Geometry). Brooks Cole, 2005. (EN)
STEIN, S. K: Calculus and analytic geometry. New York, 1989. (EN)

Recommended reading

BHUNIA, S. C., PAL, S.: Engineering Mathematics. Oxford University Press, 2015. (EN)
DANĚČEK, J. a kolektiv: Sbírka příkladů z matematiky I. CERM, 2003. (CS)
DANĚČEK, J., DLOUHÝ, O., PŘIBYL, O.: Matematika I. Modul 7 Neurčitý integrál. CERM, 2007. (CS)
DLOUHÝ, O., TRYHUK, V.: Diferenciální počet I. CERM, 2009. (CS)
NOVOTNÝ, J.: Základy lineární algebry. CERM, 2004. (CS)
SLOVAK, J., PANÁK, M., BULANT, M.: Matematika drsně a svižně. MU Brno, 2013. (CS)
TRYHUK, V. - DLOUHÝ, O.: Modul GA01_M01 studijních opor předmětu GA01. FAST VUT, Brno, 2004. [https://intranet.fce.vutbr.cz/pedagog/predmety/opory.asp] (CS)

Classification of course in study plans

  • Programme akr_BPC-SIS Bachelor's

    specialization A_SI , 1 year of study, winter semester, compulsory

  • Programme BPC-SIS Bachelor's

    specialization SI , 1 year of study, winter semester, compulsory

Type of course unit

 

Lecture

26 hours, optionally

Teacher / Lecturer

Mgr. Jana Bulantová, Ph.D.
doc. Mgr. Irena Hinterleitner, Ph.D.
Mgr. Blanka Morávková, Ph.D.
Mgr. Eva Jansová, Ph.D.

Syllabus

  1. Basics of matrix calculus, elementary transformations of a matrix, rank of a matrix.
  2. Determinants (cross rule, Sarrus' rule, Laplace expansion), rules for calculation with determinants.
  3. Vector calculus (operations with vectors, dot, cross, and mixed products of vectors). Real linear space, linear combination and independent bases and dimension of a linear space.
  4. Solutions to systems of linear algebraic equations by Gauss elimination method, Frobenius theorem.
  5. Inverse to a matrix, matrix equations. Eigenvalues and eigenvectors of a matrix.
  6. Real function of one real variable and its basic properties, explicit and parametric definition of a function. Composite function and inverse to a function. Some elementary functions (inverse trigonometric functions). 
  7. Polynomial and the basic properties of its roots, decomposition of a polynomial in the field of real and complex numbers. Rational functions and their decomposition into partial fractions.
  8. Limit of a function, continuous functions, basic theorems.
  9.  Derivative of a function, its geometric and physical applications, rules of differentiation. 
  10.  Differential of a function. Higher-order derivatives, higher-order differentials. Taylor polynomial and Taylor's theorem.
  11. L'Hospital's rule, asymptotes of the graph of a function. Sketching the graph of a function.
  12. Anti-derivative, indefinite integral and its properties. Integration by parts and substitution methods in calculating integrals.
  13. Integration of selected functions (rational, trigonometric, irrational).

Exercise

39 hours, compulsory

Teacher / Lecturer

Ing. Pavel Špaček, Dr.
Mgr. et Mgr. Jan Šafařík, Ph.D.
RNDr. Radko Odehnal
Mgr. Jana Bulantová, Ph.D.
doc. Ing. Vladislav Kozák, CSc.
RNDr. Mgr. Lucie Zrůstová, Ph.D.
doc. Mgr. Irena Hinterleitner, Ph.D.
Mgr. Blanka Morávková, Ph.D.
Mgr. Eva Jansová, Ph.D.
Mgr. Hana Boháčková, Ph.D.
Ing. Tatiana Machovičová
Mgr. Libuše Vévodová
Mgr. Margaréta Verebesová

Syllabus

  1. High school repetition.
  2. Basic operations with matrices. Elementary transformations of a matrix, rank of a matrix.
  3. Determinants (cross rule, Sarrus' rule, Laplace expansion), rules for calculation with determinants.
  4. Vector calculus (operations with vectors, dot, cross, and mixed products of vectors).
  5. Solutions to systems of linear algebraic equations by Gauss elimination method.
  6. Inverse to a matrix, matrix equations. Eigenvalues and eigenvectors of a matrix.
  7. Test 1. Some elementary functions (inverse trigonometric functions). Composite function and inverse to a function.
  8. Polynomial and the basic properties of its roots, decomposition of a polynomial in the field of real and complex numbers.
  9. Rational functions and their decomposition into partial fractions. Limit of a function, continuous functions. Derivative of a function, its geometric and physical applications, rules of differentiation.
  10. Differential of a function. Higher-order derivatives, higher-order differentials. Taylor polynomial.
  11. Test 2. L'Hospital's rule, asymptotes of the graph of a function. Sketching the graph of a function.
  12. Anti-derivative, indefinite integral and their properties. Integration by parts and substitution methods in calculating integrals.
  13. Integration of selected functions (rational, trigonometric, irrational).

Individual preparation for an ending of the course

52 hours, optionally

Teacher / Lecturer

doc. Mgr. Irena Hinterleitner, Ph.D.

Self-study

39 hours, optionally

Teacher / Lecturer

doc. Mgr. Irena Hinterleitner, Ph.D.